Bijective rigid motions of the 2D Cartesian grid

Kacper Pluta (1, 2) , Pascal Romon (1) , Yukiko Kenmochi (2) , Nicolas Passat (3)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 LIGM - Laboratoire d'Informatique Gaspard-Monge
3 CRESTIC - Centre de Recherche en Sciences et Technologies de l'Information et de la Communication - EA 3804

Rigid motions are fundamental operations in image processing. While they are bijective and isometric in R^2, they lose these properties when digitized in Z^2. To investigate these defects, we first extend a combinatorial model of the local behavior of rigid motions on Z^2, initially proposed by Nouvel and Rémila for rotations on Z^2. This allows us to study bijective rigid motions on Z^2, and to propose two algorithms for verifying whether a given rigid motion restricted to a given finite subset of Z^2 is bijective.

Domaines: Traitement des images [eess.IV]; Géométrie algorithmique [cs.CG]; Mathématique discrète [cs.DM]

Kacper Pluta, Pascal Romon, Yukiko Kenmochi, Nicolas Passat. Bijective rigid motions of the 2D Cartesian grid. Discrete Geometry for Computer Imagery (DGCI), 2016, Nantes, France. pp.359-371, ⟨10.1007/978-3-319-32360-2_28⟩. ⟨hal-01275598v2⟩